Whatever research you're doing is wrong.
And yes, samurai used katana... as a last ditch weapon if everything else went wrong, because spears, bows, and later, guns, were always much better. And even then, they didn't always use katanas. Tachi were far more popular before the era of the Ashikaga shogunate.
Katana are fine swords, don't get me wrong... but you're bullshitting yourself if they're anything incredible to speak of. Hell, this is supported by their poor metallurgic skills. Japan critically lacked access to valuable metals for a majority of it's history, which is why armor was the way it was: partially metal, but utilizing a lot of leather
Katanas are fine swords, and they cut well, but they are by no means overly superior to a broadsword and would be far less effective against more heavily armored knights like what you'd observe in Europe around the same time.
And as Recon very correctly pointed out, because this is anime, the differences between two relatively similar swords is pretty much a non-issue so the entire argument is pointless. Jaune has a shield, which helps her a lot, but the differences between a broadsword and katana really do not matter on this level. Swap one out for a spear, and you have a different story.